A new fixed-time stability theorem and its application to the fixed-time synchronization of neural networks

Chen, Chuan; Li, Lixiang; Peng, Haipeng; Yang, Yixian; Mi, Ling; Zhao, Hui

doi:10.1016/j.neunet.2019.12.028

Cited by 172 publications

(64 citation statements)

References 34 publications

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“…Thus, the origin of system (1) is fixed-time stable, and the settling time T (x 0 ) is estimated by (6). This is complete proof.…”

Section: Fixed-time Stabilitymentioning

confidence: 62%

“…respectively. According to Theorem 2 and Theorem 4, one has T 6 max > T * 3 max , T 7 max > T * 3 max . Therefore T * 3 max owns higher precise.…”

Section: Remarkmentioning

confidence: 93%

“…Since [2] derived some criteria on the fixed-time stability of nonlinear systems and estimates of the settling time, there has been a lot of results about fixed-time stability of nonlinear system [3]- [6]. For example, [4] investigates fixedtime convergence of system by means of inverse function of Lyapunov function.…”

Section: Introductionmentioning

confidence: 99%

“…For example, [4] investigates fixedtime convergence of system by means of inverse function of Lyapunov function. In [5] and [6], two new fixed-time stability theorems are proposed. In virtue of reduction to absurdity, a theorem of fixed-time stability is established and a higher-precision estimate of the settling-time is proposed in [7].…”

Section: Introductionmentioning

confidence: 99%

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Fixed-Time Stabilization of Nonlinear System and its Application into General Neural Networks

Yan

2020

IEEE Access

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In this paper, fixed-time stability problem of nonlinear system is investigated. Firstly, a new fixed-time stability theorem is established, and a higher precise estimate of settling time is provided. Secondly, by theoretical deduction, the provided estimate is compared with the ones in existing fixedtime stabiity theorems. It is shown that our estimate is less conservative and more accurate than existing results. Moreover, as a practical application, fixed-time stabilization problem of general neural networks is studied. By developing a framework of protocol and applying the new fixed-time stability theorem, some new criteria are derived to solve fixed-time stabilization problem of general neural networks systems. Finally, two simulation examples are provided to verify the validity of our theoretical results. INDEX TERMS Fixed-time stability, Filippov solution, general neural networks, settling time.

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“…Thus, the origin of system (1) is fixed-time stable, and the settling time T (x 0 ) is estimated by (6). This is complete proof.…”

Section: Fixed-time Stabilitymentioning

confidence: 62%

“…respectively. According to Theorem 2 and Theorem 4, one has T 6 max > T * 3 max , T 7 max > T * 3 max . Therefore T * 3 max owns higher precise.…”

Section: Remarkmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fixed-Time Stabilization of Nonlinear System and its Application into General Neural Networks

Yan

2020

IEEE Access

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“…Next, we list several existing results for finite-time stability and fixed-time stability of (1) by using Lyapunov functions. Lemma 1 (42). If there exists a function V ∶ R n → R max belongs to the class  (i-e V is continuous and strictly increasing and V(y) = 0 implies that y = 0) such that any solution of (1) satisfies following the inequalitẏ V(y(t)) ≤ −bV (y(t)) − cV (y(t))…”

Section: Preliminaries and Model Descriptionmentioning

confidence: 99%

New feedback control techniques of quaternion fuzzy neural networks with time‐varying delay

Aouiti

Jallouli

2021

Intl J Robust & Nonlinear

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This article addresses the problems of fixed-time stabilization for a class of quaternion fuzzy neural networks (QFNNs) with time-varying delay. The QFNNs are developed by dividing our system into four real-valued parts based on the Hamilton rule. Then, based on fixed-time stability theory, some inequality techniques, and selecting the appropriate controllers and Lyapunov function, a novel criterion guaranteeing the fixed-time stabilization and the finite-time stabilization of the addressed system is derived. Finally, three numerical examples are presented to show the effectiveness of our theoretical results. K E Y W O R D S finite-time stabilization, fixed-time stabilization, fuzzy neural networks, quaternion neural networks, time-varying delay

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Fixed time function combination synchronization of perturbed chaotic systems via adaptive control

Su,

Luo

2024

Adaptive Control & Signal

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SummaryThe concerns of this article is to investigate the fixed time function combination synchronization (FCS) among three different chaotic systems with disturbances. First, a new stability theorem is presented by virtue of the integral inequality technique and a more accurate upper estimation of the convergence time is given. Next, the fixed time FCS problem is considered for the perturbed chaotic systems in which the scaling functions are generated by the bounded dynamical systems. Besides, the synchronization time is related to the control parameters rather than the initial values. The time upper bound can be calculated out by the simple formula, which is the function of control parameters. Finally, a simulation example is provided to illustrate the correctness of the derived criteria.

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A new fixed-time stability theorem and its application to the fixed-time synchronization of neural networks

Cited by 172 publications

References 34 publications

Fixed-Time Stabilization of Nonlinear System and its Application into General Neural Networks

Fixed-Time Stabilization of Nonlinear System and its Application into General Neural Networks

New feedback control techniques of quaternion fuzzy neural networks with time‐varying delay

Fixed time function combination synchronization of perturbed chaotic systems via adaptive control

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